Influenza Bern

Methoods

Incidence and Reproduction number ( R effective)

  • Incidence per 1’000 inhabitants
  • Rolling average over 3 weeks

Maps - Municipalities

  • calculated only for pandemic times:
    • 21.06.1918 - 20.09.1918
    • 27.09.1918 - 20.06.1919
    • 02.01.1920 - 18.06.1920
    • 23.12.1921 - 05.05.1922
    • 11.01.1924 - 30.05.1924
    • 12.12.1924 - 08.05.1925
  • Incidence:
    • breaks: Jenks Natural Breaks - finds the “best” way to split up the ranges.
    • natural breaks minimizes the variation within each color, so the areas within each color are as close as possible in value to each other
    • quantile breaks do not work, because there are many zeros in the municipalities from 1920 onwards
  • Hotspots:
    • local spatial statistic G
    • R package: spdep
    • returned is a Z-value
    • high positive values indicate the posibility of a local cluster of high values
    • low relative values a similar cluster of low values

Co-factors for Pandemic 1918/1919

  • sum of all cases per municipality for 1918 and 1919
  • Incidence per 1’000 inhabitants
  • Negative binomial regression to avoid over dispersion
  • bivariate maps



The following co-factors were considered:
* Population density * Altitude * Precipitation -> However,altitude and precipitation are highly correlated. There is a significant interaction between altitude and precipitation. For that reason I would take only the altitude as co-factor for the total number of cases 1918/1919 * TB death * Proportion of people working in agriculture and industry, I would take only one (same result only opposite) * Proportion of “Betriebe”, “Anzahl Arbeiter in den Betriebe”, “PS”. 194 municipalities does not have any Betriebe * Urbanity, only 3 cities -> not possible to use with this classification

For bivarite map clustering “quantile” clustering was used for population density, altitude, precipitation, tb death and proportion of people working in industry and agriculture.

Since “Betriebe”, “Anzahl Arbeiter in den Betriebe” and “PS” have a lot of zeros (no Beriebe) “quantile” clustering is not possible, therefor “jenks” was used.

Canton Bern

Regions of Bern

Incidence

Municipality

1918 First wave

1918-1919 second wave

1920

1922

1924

End 1924 -1925

Co-factors

Population density

Municipality with a higher population density have a significant higher incidence.

## 
## Call:
## glm.nb(formula = Sum_date ~ PopDens + offset(log(Population)), 
##     data = data_inc, link = "log", init.theta = 1.608201514)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.5711  -0.9305  -0.1815   0.4678   2.9240  
## 
## Coefficients:
##               Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -1.9043444  0.0438796 -43.399  < 2e-16 ***
## PopDens      0.0005417  0.0001802   3.006  0.00265 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Negative Binomial(1.6082) family taken to be 1)
## 
##     Null deviance: 521.57  on 463  degrees of freedom
## Residual deviance: 515.22  on 462  degrees of freedom
##   (11 Beobachtungen als fehlend gelöscht)
## AIC: 5279.4
## 
## Number of Fisher Scoring iterations: 1
## 
## 
##               Theta:  1.608 
##           Std. Err.:  0.102 
## 
##  2 x log-likelihood:  -5273.438

## PopDens breaks (x-axis):
## style: quantile
##          [0,69.362)   [69.362,122.6337) [122.6337,3306.645] 
##                 155                 154                 155 
## Sum_Inc breaks (y-axis):
## style: quantile
##        [0,90.57187) [90.57187,193.4673)  [193.4673,815.047] 
##                 158                 158                 159

Altitude

There is a significant correlation between the altitude and the incidence. The higher the municipality, the lower the incidence.

## 
## Call:
## glm.nb(formula = Sum_date ~ HöheüM + offset(log(Population)), 
##     data = data_inc, link = "log", init.theta = 1.605654021)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.5418  -0.9377  -0.1644   0.4215   3.5664  
## 
## Coefficients:
##               Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -1.4731187  0.1314764 -11.204  < 2e-16 ***
## HöheüM      -0.0005792  0.0002035  -2.846  0.00443 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Negative Binomial(1.6057) family taken to be 1)
## 
##     Null deviance: 534.35  on 473  degrees of freedom
## Residual deviance: 525.81  on 472  degrees of freedom
##   (1 Beobachtung als fehlend gelöscht)
## AIC: 5373.9
## 
## Number of Fisher Scoring iterations: 1
## 
## 
##               Theta:  1.606 
##           Std. Err.:  0.101 
## 
##  2 x log-likelihood:  -5367.883

## HöheüM breaks (x-axis):
## style: quantile
##       [328,511)  [511,655.3333) [655.3333,1356] 
##             157             159             158 
## Sum_Inc breaks (y-axis):
## style: quantile
##        [0,90.57187) [90.57187,193.4673)  [193.4673,815.047] 
##                 158                 158                 159

Precipitation

There is a significant correlation between Precipitation and the incidence. The more precipitation, the lower the incidence. Altitude and precipitation show a significant interaction. I would not show precipitation for total cases per municipility.

## 
## Call:
## glm.nb(formula = Sum_date ~ Total_rain + offset(log(Population)), 
##     data = data_inc, link = "log", init.theta = 1.631214115)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.6272  -0.9140  -0.1511   0.4149   3.5085  
## 
## Coefficients:
##               Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -4.913e-01  3.739e-01  -1.314 0.188896    
## Total_rain  -2.352e-05  6.500e-06  -3.619 0.000295 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Negative Binomial(1.6312) family taken to be 1)
## 
##     Null deviance: 528.59  on 463  degrees of freedom
## Residual deviance: 514.84  on 462  degrees of freedom
##   (11 Beobachtungen als fehlend gelöscht)
## AIC: 5272.2
## 
## Number of Fisher Scoring iterations: 1
## 
## 
##               Theta:  1.631 
##           Std. Err.:  0.104 
## 
##  2 x log-likelihood:  -5266.180

## Total_rain breaks (x-axis):
## style: quantile
## [44667.56,53635.27)  [53635.27,59236.5)  [59236.5,83922.42] 
##                 155                 154                 155 
## Sum_Inc breaks (y-axis):
## style: quantile
##        [0,90.57187) [90.57187,193.4673)  [193.4673,815.047] 
##                 158                 158                 159

Tuberculosis death

No evidence of a significant association, but trend that high TB deaths lead to lower incidence.

## 
## Call:
## glm.nb(formula = Sum_date ~ TB + offset(log(Population)), data = data_inc, 
##     link = "log", init.theta = 1.66651015)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.0214  -0.9303  -0.1777   0.4702   2.8453  
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -1.735347   0.092073 -18.847   <2e-16 ***
## TB          -0.004045   0.003396  -1.191    0.234    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Negative Binomial(1.6665) family taken to be 1)
## 
##     Null deviance: 510.06  on 461  degrees of freedom
## Residual deviance: 508.53  on 460  degrees of freedom
##   (13 Beobachtungen als fehlend gelöscht)
## AIC: 5239.3
## 
## Number of Fisher Scoring iterations: 1
## 
## 
##               Theta:  1.667 
##           Std. Err.:  0.106 
## 
##  2 x log-likelihood:  -5233.349

## TB breaks (x-axis):
## style: quantile
##        [0,19.3) [19.3,28.83333) [28.83333,75.9] 
##             151             157             154 
## Sum_Inc breaks (y-axis):
## style: quantile
##        [0,905.7187) [905.7187,1934.673)  [1934.673,8150.47] 
##                 158                 158                 159

people working in agriculture

There is no evidence for a significant association between the proportion of people working in agriculture and incidence.

## 
## Call:
## glm.nb(formula = Sum_date ~ Lws_prop + offset(log(Population)), 
##     data = data_inc, link = "log", init.theta = 1.584206326)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.5657  -0.9249  -0.1971   0.4560   2.8253  
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -1.784345   0.085843 -20.786   <2e-16 ***
## Lws_prop    -0.001947   0.003668  -0.531    0.596    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Negative Binomial(1.5842) family taken to be 1)
## 
##     Null deviance: 524.52  on 471  degrees of freedom
## Residual deviance: 524.22  on 470  degrees of freedom
##   (3 Beobachtungen als fehlend gelöscht)
## AIC: 5354.3
## 
## Number of Fisher Scoring iterations: 1
## 
## 
##               Theta:  1.5842 
##           Std. Err.:  0.0994 
## 
##  2 x log-likelihood:  -5348.2770

## Lws_prop breaks (x-axis):
## style: quantile
## [0.456621,16.74419) [16.74419,25.64935) [25.64935,72.72727] 
##                 157                 157                 158 
## Sum_Inc breaks (y-axis):
## style: quantile
##        [0,90.57187) [90.57187,193.4673)  [193.4673,815.047] 
##                 158                 158                 159

people working in industry

There is no evidence for a significant association between the proportion of people working in agriculture and incidence.

## 
## Call:
## glm.nb(formula = Sum_date ~ Gew_prop + offset(log(Population)), 
##     data = data_inc, link = "log", init.theta = 1.583275675)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.5747  -0.9251  -0.1909   0.4519   2.7685  
## 
## Coefficients:
##               Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -1.8378980  0.0766667 -23.973   <2e-16 ***
## Gew_prop     0.0008383  0.0044558   0.188    0.851    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Negative Binomial(1.5833) family taken to be 1)
## 
##     Null deviance: 524.23  on 471  degrees of freedom
## Residual deviance: 524.19  on 470  degrees of freedom
##   (3 Beobachtungen als fehlend gelöscht)
## AIC: 5354.5
## 
## Number of Fisher Scoring iterations: 1
## 
## 
##               Theta:  1.5833 
##           Std. Err.:  0.0993 
## 
##  2 x log-likelihood:  -5348.5350

## Gew_prop breaks (x-axis):
## style: quantile
##        [0,10.57402) [10.57402,18.25813) [18.25813,55.44958] 
##                 157                 157                 158 
## Sum_Inc breaks (y-axis):
## style: quantile
##        [0,90.57187) [90.57187,193.4673)  [193.4673,815.047] 
##                 158                 158                 159

Industrial companies

There is no evidence for a significant association between the numbers of industrual companies per 1’000 inhabitants and incidence. However 194 municipality does not have any industrial companies. Grouping the “companies” in two (or more groups (e.g. none, same, a lot)) give the same result.

## 
## Call:
## glm.nb(formula = Sum_date ~ Betriebe_prop + offset(log(Population)), 
##     data = data_inc, link = "log", init.theta = 1.565436317)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.5574  -0.9140  -0.1872   0.4503   2.7331  
## 
## Coefficients:
##               Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   -1.83921    0.04183 -43.970   <2e-16 ***
## Betriebe_prop  0.01106    0.02139   0.517    0.605    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Negative Binomial(1.5654) family taken to be 1)
## 
##     Null deviance: 529.67  on 474  degrees of freedom
## Residual deviance: 529.42  on 473  degrees of freedom
## AIC: 5390.1
## 
## Number of Fisher Scoring iterations: 1
## 
## 
##               Theta:  1.5654 
##           Std. Err.:  0.0981 
## 
##  2 x log-likelihood:  -5384.0630

## Betriebe_prop breaks (x-axis):
## style: jenks
##   one of 11,325 possible partitions of this variable into 3 classes
##        [0,1.267427] (1.267427,4.166667] (4.166667,9.393451] 
##                 363                  80                  32 
## Sum_Inc breaks (y-axis):
## style: jenks
##        [0,150.7353] (150.7353,346.7742]  (346.7742,815.047] 
##                 260                 185                  30

Total workers

There is no evidence for a significant association between the numbers of workers per 1’000 inhabitants and incidence. However 194 municipality does not have any industrial companies. Grouping the “total workers” in two (or more groups (e.g. none, same, a lot)) give the same result.

## 
## Call:
## glm.nb(formula = Sum_date ~ Arbeiter_prop + offset(log(Population)), 
##     data = data_inc, link = "log", init.theta = 1.566256701)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.5565  -0.9201  -0.1972   0.4557   2.7423  
## 
## Coefficients:
##                Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   -1.842947   0.041203 -44.728   <2e-16 ***
## Arbeiter_prop  0.003399   0.004508   0.754    0.451    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Negative Binomial(1.5663) family taken to be 1)
## 
##     Null deviance: 529.93  on 474  degrees of freedom
## Residual deviance: 529.41  on 473  degrees of freedom
## AIC: 5389.8
## 
## Number of Fisher Scoring iterations: 1
## 
## 
##               Theta:  1.5663 
##           Std. Err.:  0.0981 
## 
##  2 x log-likelihood:  -5383.7950

## Arbeiter_prop breaks (x-axis):
## style: jenks
##        [0,6.944444] (6.944444,21.84497] (21.84497,59.08184] 
##                 391                  58                  26 
## Sum_Inc breaks (y-axis):
## style: jenks
##        [0,150.7353] (150.7353,346.7742]  (346.7742,815.047] 
##                 260                 185                  30

PS

There is no evidence for a significant association between PS per 1’000 inhabitants and incidence. However 194 municipality does not have any industrial companies. Grouping the “PS” in two (or more groups (e.g. none, same, a lot)) give the same result.

## 
## Call:
## glm.nb(formula = Sum_date ~ PS + offset(log(Population)), data = data_inc, 
##     link = "log", init.theta = 1.571974792)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.5617  -0.9130  -0.1840   0.4496   2.7773  
## 
## Coefficients:
##               Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -1.842e+00  3.773e-02  -48.83   <2e-16 ***
## PS           7.967e-05  5.044e-05    1.58    0.114    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Negative Binomial(1.572) family taken to be 1)
## 
##     Null deviance: 531.74  on 474  degrees of freedom
## Residual deviance: 529.37  on 473  degrees of freedom
## AIC: 5387.9
## 
## Number of Fisher Scoring iterations: 1
## 
## 
##               Theta:  1.5720 
##           Std. Err.:  0.0985 
## 
##  2 x log-likelihood:  -5381.9420

## PS_prop breaks (x-axis):
## style: jenks
##   one of 11,026 possible partitions of this variable into 3 classes
##        [0,27.50432] (27.50432,124.0506] (124.0506,380.5073] 
##                 452                  22                   1 
## Sum_Inc breaks (y-axis):
## style: jenks
##        [0,150.7353] (150.7353,346.7742]  (346.7742,815.047] 
##                 260                 185                  30